Problem: Solve for $x$ and $y$ using substitution. ${-6x-5y = 3}$ ${y = 2x-7}$
Answer: Since $y$ has already been solved for, substitute $2x-7$ for $y$ in the first equation. ${-6x - 5}{(2x-7)}{= 3}$ Simplify and solve for $x$ $-6x-10x + 35 = 3$ $-16x+35 = 3$ $-16x+35{-35} = 3{-35}$ $-16x = -32$ $\dfrac{-16x}{{-16}} = \dfrac{-32}{{-16}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 2x-7}\thinspace$ to find $y$ ${y = 2}{(2)}{ - 7}$ $y = 4 - 7$ $y = -3$ You can also plug ${x = 2}$ into $\thinspace {-6x-5y = 3}\thinspace$ and get the same answer for $y$ : ${-6}{(2)}{ - 5y = 3}$ ${y = -3}$